Title: Assistant Clinical Professor, Psychiatry and Biomathematical Sciences
Institution: Mount Sinai School of Medicine
Street: 1 Gustave L. Levy Place
City: New York
Phone: (212) 241-3843
Fax: (646) 728-4685
Authors: James Schmeidler
Title: Improved Algorithms for Closure
Abstract: In a stepdown procedure for testing the homogeneity of all subsets of k means, closure improves power, but requires many additional tests. For every partition of all k means, there is a composite null hypothesis that all sets in the partition are homogeneous. Homogeneity of a subset of p means is rejected by closure if all composite hypotheses that include the subset are rejected. The Begun and Gabriel (1981) closure algorithm tests only the subset and 2^m - m - 1 subsets of the m = k - p complementary means. An improved closure algorithm tests only the m - 1 pairs of adjacent complementary means. It is valid for unbalanced analysis of variance tests, and for Studentized range tests except in extremely unbalanced designs. Seaman, Levin, and Serlin (1991) improved power for closure. However, their procedure tests composite hypotheses; it cannot exploit the Begun and Gabriel algorithm. A new algorithm tests only composite hypotheses not rejected based ! on Begin and Gabriel algorithm results. Testing any composite hypotheses is not necessary if only one complementary subset is not heterogeneous by the Begin and Gabriel algorithm.
References: Begun, J. and Gabriel, K. R. (1981), "Closure of the Newman-Keuls Multiple Comparisons Procedure," Journal of the American Statistical Association, 76, 241-245.
Seaman, M.A., Levin, J. R., and Serlin, R. C. (1991), "New Developments in Pairwise Multiple Comparisons: Some Powerful and Practical Procedures," Psychological Bulletin, 110, 577-586.